which was first introduced by Greenspan in 1978 [1]}. This equation describes the surface-tension-dominated motion of thin viscous films for the film height \(u(t, x)\)  and spreading droplets in the lubrication approximation [1]}. In particular, for \(\alpha =3\)  it describes a classical thin film of Newtonian fluid, as reviewed in [3]}, \(\alpha =1\)  occurs in the dynamics of a Hele-Shaw cell [4]}
and \(\alpha =2\)  arises in a study of wetting films with a free contact line between film and substrate [5]}. There also exist many interesting generalizations of the famous equation (REF ) (see [6]}, [7]} and reference therein).
